Deck 13: Interest Rate Forwards and Options

Question 1

The payoff to the holder of a long FRA on 90-day LIBOR with a fixed rate of 8.75 percent,a notional principal of $20 million if the underlying is 9 percent at expiration is

A)$12,500
B)-$12,500
C)-$12,225
D)$12,225
E)-$48,900

Answer 1

D

Question 2

Find the rate on a pure discount loan hedged with a long FRA if the loan is for $10 million and matures in 30 days,the FRA is 30-day LIBOR,the fixed rate on the FRA is 4 percent,and LIBOR at the time the loan is taken out is 5 percent.

A)4.87 percent
B)0.25 percent
C)5.18 percent
D)3.10 percent
E)2.04 percent

Answer 2

D

Question 3

A bank makes a $5 million 180-day pure discount loan at LIBOR of 9 percent.At the same time,however,it exercises an interest rate put that has a strike of 11 percent.Find the annualized rate of return on the loan.Ignore the cost of the put.

A)9.34 percent
B)11.47 percent
C)9 percent
D)11 percent
E)none of the above

Answer 3

B

Question 4

Which of the following is a limitation of using the Black model to price interest rate options?

A)the risk-free rate is not constant
B)the volatility is not constant
C)interest rates are not lognormally distributed
D)all of the above
E)none of the above

Question 5

An FRA in which the rate is not set according to rates in the market is called

A)a short FRA
B)a long FRA
C)an off-market FRA
D)a hedged FRA
E)an FRA spread

Question 6

A bank buys an interest rate floor in conjunction with a loan it holds that will make four semiannual payments starting six months from now.The floor has a strike of 9 percent.LIBOR at the beginning of the four payment periods is 10,11,8,and 8.6 percent.On which dates will the floor writer make a payment to the bank?

A)now and in 24 months
B)in 18 and 24 months
C)in 12 and 18 months
D)in 6,12,18 and 24 months
E)none of the above

Question 7

Find the payoff of an interest rate call option on the annual rate with an exercise rate of 10 percent if the one-period rate at expiration is 11 percent.(No days/360 adjustment is necessary and assume a $1 notional principal. )

A)0.12
B)zero
C)0.01
D)0.0090
E)none of the above

Question 8

Which of the following is not required to determine a swaption payoff at expiration?

A)the exercise rate
B)the term structure of zero coupon rates at the swaption expiration
C)the maturity of the underlying swap
D)the yield on a bond of equivalent maturity as the swap
E)none of the above

Question 9

An FRA differs from an interest rate swap in which of the following ways?

A)An FRA has more credit risk
B)FRAs are federally regulated
C)Traditionally the payment in an FRA is delayed
D)FRAs are used only by banks and swaps are used only by corporations
E)none of the above

Question 10

Find the approximate market value of a long position in an FRA at a fixed rate of 5 percent in which the contract expires in 20 days,the underlying is 180-day LIBOR,the notional principal is $25 million,the 20-day rate is 7 percent,and the 200-day rate is 8.5 percent.

A)$433,658
B)-$454,954
C)$322,819
D)-$322,819
E)$454,954

Question 11

Determine the value of an interest rate call option at the maturity of a loan if the call has a strike of 12 percent,a face value of $50 million,the loan matures 90 days after the call is exercised,the call expires in 60 days,the call premium is $200,000,and LIBOR ends up at 13 percent.

A)$125,000
B)$83,333
C)$208,000
D)-$75,000
E)none of the above

Question 12

Which of the following is a 1 x 4 FRA?

A)The FRA expires in one month,and the underlying Eurodollar expires in three months.
B)The FRA expires in four months,and the underlying Eurodollar expires in one month.
C)The FRA expires in one month,and the underlying Eurodollar expires in four months.
D)The FRA expires in three months,and the underlying Eurodollar expires in four months.
E)The FRA expires in one month,and the underlying Eurodollar expires in five months.

Question 13

Which of the following strategies replicates a long position in an FRA?

A)long a long term Eurodollar time deposit and short a short-term Eurodollar time deposit
B)long a Eurodollar futures and short a Eurodollar option
C)long a Eurodollar option on a futures
D)short a long-term Treasury bond futures and short a short-term Treasury bond futures
E)long a receiver swaption

Question 14

Find the premium of a correctly priced interest rate call on 30-day LIBOR if the current forward rate is 7 percent,the strike is 7 percent,the continuously compounded risk-free rate is 6.2 percent,the volatility is 12 percent and the option expires in one year.The notional principal is $30 million.

A)$.0031
B)$93,000
C)$7,817
D)$0.0012
E)$36,000

Question 15

Which of the following best describes an interest rate cap?

A)a cash-and-carry hedge
B)a series of forward contracts
C)a series of interest rate calls
D)a call option spread
E)none of the above

Question 16

The advantage of a collar over a cap is

A)it lowers the out-of-pocket cost
B)it offers the possibility of greater returns
C)it eliminates the risk
D)it has lower transaction costs
E)none of the above

Question 17

A payer swaption is equivalent to which of the following instruments.

A)a call option on a bond
B)a long Treasury bond futures option
C)a long Eurodollar futures
D)an interest rate cap
E)a put option on a bond

Question 18

The fixed rate on an FRA expiring in 30 days on 180-day LIBOR with the 30-day rate being 5 percent and the 210 day rate being 6 percent is

A)6 percent
B)6.14 percent
C)5 percent
D)5.5 percent
E)5.15 percent

Question 19

Swaptions are like forward swaps in which of the following ways

A)Both are free of credit risk
B)Both require the execution of a swap at expiration
C)They have the same price
D)Both are traded on swaption exchanges
E)none of the above

Question 20

An FRA is most like which of the following transactions

A)an interest rate cap
B)an interest rate floor
C)an interest rate collar
D)a forward contract
E)none of the above

Question 21

Buying an interest rate call results in a limited loss if interest rates fall.

Question 22

All of the following are uses of swaptions except

A)to speculate on interest rates
B)to give a firm flexibility in future borrowings
C)to borrow money
D)to create callable from non-callable bonds
E)none of the above

Question 23

An interest rate payer swaption is more like an interest rate put than an interest rate call.

Question 24

When pricing interest rates in the Black model,the underlying is the forward rate.

Question 25

Find the fixed rate on a forward swap expiring in 90 days in which the underlying swap has a maturity of 180 days and makes payments every 90 days.The prices of zero coupon bonds are 0.9877 (90 days),0.9732 (180 days),and 0.9597 (270 days).

A)5.97 percent
B)5.6 percent
C)5.5 percent
D)5.78 percent
E)5 percent

Question 26

An interest rate collar is the purchase of a cap and a floor.

Question 27

The pricing of a forward swap is done in the same manner as pricing a spot started today,except that forward rates are used instead of spot rates.

Question 28

If a lender uses a collar,the transactions would be

A)buy a floor at one exercise price,sell a floor at another exercise price
B)buy a floor,sell a cap
C)sell a floor,buy a cap
D)buy a cap at one exercise price,sell a floor at another exercise price
E)buy a cap and sell a floor at the same exercise price

Question 29

The payoff of a long interest rate floor is equivalent to the payoff of a short receiver swaption.

Question 30

A payer swaption is expiring.The underlying swap has a two year maturity.Th e present value factors are 0.9259 (one year)and 0.8651 (two years).The strike rate is 7 percent.What is the value of the swaption per $1 notional principal.

A)0.0000,since it is out-of-the-money
B)1.0000
C)0.0753
D)0.0095
E)none of the above

Question 31

Pricing an interest rate cap is done by pricing the component caplets and adding up their values.

Question 32

If interest rates increase,the holder of a long FRA benefits.

Question 33

The Black model's accuracy in pricing interest rate options is greatest when the options have short maturities.

Question 34

For firms that may need to enter into a swap in the future,a forward swap serves as well as a swaption.

Question 35

The convention for calculating interest on an interest rate derivative is to multiply the notional principal times the payoff function times 90 over 360 or 365.

Question 36

FRA payoffs are discounted by the current interest rate.

Question 37

In a zero cost collar,the exercise price on the floor is set such that the floor premium more than offsets the cap premium.

Question 38

A long interest rate cap is an appropriate strategy for a party that lends money.

Question 39

Payer swaptions can be used to hedge put features on bonds.

Question 40

A short FRA would be appropriate for a party anticipating an increase in interest rates.

Question 41

Payer swaptions can be used to convert callable to non-callable debt.

Question 42

FRAs,and caps and floors are guaranteed against default.

Question 43

The appropriate fixed rate on an FRA is the forward rate in the term structure.

Question 44

In a 12 x 18 FRA,the derivative expires in one year and the underlying matures in 18 months.

Question 45

Receiver swaptions allow a firm to receive a floating rate.

Question 46

A long cap and a long floor with the exercise price set at the swap rate is equivalent to a swap.

Question 47

In an FRA on an m-day rate,payment is made when the interest rate is determined rather than m days later.

Question 48

An off-market FRA is one constructed outside of the over-the-counter market.

Question 49

Interest rate caps are equivalent to a series of interest rate call options.